This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380278 #15 Jan 24 2025 19:40:52 %S A380278 1,2,1,3,1,4,1,3,5,6,4,3,7,8,5,3,6,9,10,3,5,11,8,3,12,13,5,3,14,10,15, %T A380278 3,5,11,16,3,17,12,5,3,10,18,19,3,5,11,15,3,20,21,5,3,22,23,17,3,5,11, %U A380278 24,3,18,25,5,3,26,27,28,3,5,11,29,3,17,30,5,3,31 %N A380278 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by exactly k terms and each subsequence enclosed by consecutive equal values is distinct. %C A380278 Does each value occur finitely many times? %C A380278 Since the length of a subsequence is given by its enclosing values, the sequence remains the same whether we include those endpoints or not when checking the uniqueness of subsequences. %H A380278 Neal Gersh Tolunsky, <a href="/A380278/b380278.txt">Table of n, a(n) for n = 1..10000</a> %e A380278 a(9) = 5: a(9) cannot be 1 because this would create the subsequence a(7..9) = 1,3,1 enclosing [3], which would repeat a(3..5) = 1,3,1 enclosing [3] again. a(9) cannot be 2 because this would not enclose 2 terms with the previous occurrence of 2. For the same reason, 3 and 4 do not work. a(9) can be the first occurrence of 5 without restriction. So a(9) = 5. %Y A380278 Cf. A026272. %K A380278 nonn %O A380278 1,2 %A A380278 _Neal Gersh Tolunsky_, Jan 18 2025